SUMMARY

Hagfish are able to produce substantial amounts of slime when harassed, but
the precise ecological function of the slime is unclear. One possibility is
that the slime acts as a defence against gill-breathing predators, whose gills
may become entangled with the slime's mixture of mucins and fibrous threads
during an attack. We previously demonstrated that hagfish slime does not bind
water tightly, but instead behaves like a fine sieve that slows water down
via viscous entrainment. These properties are consistent with the
gill-clogging hypothesis, which we tested here by quantifying the effects of
hagfish slime on water flow through an artificial gill model and real fish
gills. Our results indicate that the slime is capable of clogging gills and
increasing the resistance that they present to the flow of water. We also
characterized the behaviour of slime release from live hagfish and the effect
of convective mixing on the formation of slime in vitro. Our
observations show that exudate is locally released from the slime glands as a
coherent jet and that hagfish do not appear to use their slime as a protective
envelope. We found that convective mixing between the exudate and seawater is
necessary for proper slime formation, but excessive mixing leads to the
slime's collapse. We suggest that the loose binding of water by the slime may
be an optimal solution to the problem of delivering an expanding jet of
flow-inhibiting material to the gills of would-be predators.

Introduction

An agitated hagfish can release an enormous amount of slime from the
numerous slime glands lining its body
(Ferry, 1941;
Strahan, 1959;
Downing et al., 1981a;
Martini, 1998). In a previous
paper (Fudge et al., 2005), we
demonstrated that hagfish slime is an extremely dilute assemblage of mucins
and seawater held together by a network of fine protein threads. Measurements
of water egress from hagfish slime indicated that it is not a coherent
material that immobilizes water, but instead a fine sieve that slows water
down via viscous entrainment. These experiments, along with the many
papers on hagfish slime by the late Elizabeth Koch and other researchers
(Downing et al., 1981b;
Fernholm, 1981;
Koch et al., 1991;
Fudge et al., 2003), answer
several questions about slime morphology and mechanics. However, fundamental
questions about the function of the slime persist.

The list of common hagfish predators includes certain species of seabirds,
pinnipeds and cetaceans but exhibits a conspicuous lack of fishes
(Martini, 1998;
Fudge, 2001). This fact has led
researchers to speculate that the slime functions as a defence against
gill-breathing predators by clogging the gills
(Fernholm, 1981;
Martini, 1998). The mechanical
data we report in Fudge et al.
(2005) on slime formed in
vitro do not contradict this hypothesis. We found that the threads within
hagfish slime are extremely effective at catching on projections and making
continuous connections across substantial distances. While the slime does not
possess the coherence of a solid material, it is capable of trapping large
volumes of water via viscous entrainment. From these data it is not
difficult to imagine that the slime would attach easily to gills and seriously
impair respiratory flow across them. Here, we test the gill-clogging
hypothesis by measuring the effect of hagfish slime on water flow through an
artificial gill analogue and real gills in isolated fish heads and demonstrate
that the slime has dramatic effects on flow at physiological water pressures.
We also provide information from high-speed video trials on the details of
slime release and formation by free-swimming hagfish.

Materials and methods

Experimental animals

Pacific hagfish (Eptatretus stoutii Lockington) were collected
from Barkley Sound in British Columbia with the assistance of local staff at
the Bamfield Marine Sciences Centre. Traps baited with herring were set at a
bottom depth of approximately 100 m and left overnight. Hagfish were
transported to the University of British Columbia, transferred to a 200-litre
holding aquarium of cold seawater (9°C, 34%thou) and given a monthly diet
of squid in accordance with UBC Committee on Animal Care guidelines (protocol
A2-0003).

Apparatus for measuring the effects of hagfish slime on flow rate through
and resistance across an artificial gill analogue, which consisted of a piece
of test tube brush within polyvinyl tubing. Scale bar, 10 mm.

(A) Apparatus for measuring the effect of hagfish slime on flow through
fish gills, consisting of a severed rockfish head with its mouth propped open
and housed in PVC piping. (B) Front view.

Slime effects on gills

We modelled a gill-breathing predator with two versions of a custom-built
`slime vacuum' that used a siphon to create water flow over an artificial gill
analogue and real fish gills. The artificial gills consisted of a 40 mm-long
piece of test tube brush inserted inside a 165 mm segment of thick, clear
polyvinyl tubing (20 mm inner diameter). The brush was positioned
approximately 40 mm from one end of the tube and fitted snugly inside
(Fig. 1). The heads from
freshly dead China rockfish (Sebastes nebulosus Ayres) from a local
supermarket provided real gills. Fish had a mean (± s.d.) body mass of
577±118 g and mouth gape area of 580±40 mm2. The head
was severed from the body just anterior to the dorsal fin, and any remaining
fins and spines were removed. The isolated fish head was housed within a piece
of PVC pipe (150 mm length, 100 mm diameter) fitted with a sheet of
extra-heavy dental dam (152×152 mm; Hygenic Corp., Akron, OH, USA) at
one end. The head was pushed from the inside of the pipe through a small hole
in the dental dam to a point just posterior of the eyes and anterior to the
gill operculum (Fig. 2A,B).
Heads that were too large to fit inside the pipe had a dorsal portion of
muscle removed after severing. A wire oval ring was used to prop the mouth
open and hold the tongue down, and small corks were positioned at the front of
each opercular cavity to slightly open the opercular flaps. Rubber bands and
string wrapped around the edge of the dental dam encircling the head ensured a
tight seal. A screw cap closed the other end of the PVC pipe, and a hole in
the side provided a passage for water flow out of the pipe.

A series of tubing formed the rest of both versions of the slime vacuum.
Each gill setup was connected to polyvinyl tubing (1.52 m long, 8 mm inner
diameter) followed by a short segment of rubber tubing (225 mm long, 6.6 mm
inner diameter), which could be clamped to restrict water flow. Screw adapters
joined the consecutive pieces. Experiments were held in a 20-litre aquarium of
cold artificial seawater (8-10°C, 32%thou). For artificial gill trials,
the gill setup was attached to a plastic rod and held in position underwater
by clamping the rod to the rim of the aquarium. In fish head trials, the
apparatus was kept in place at one end of the aquarium with bricks. A bucket
on a top-loading balance placed below the aquarium collected the siphoned
water. The free end of the rubber tubing rested in a small overflowing beaker
positioned directly above the bucket, reducing the incidence of air bubbles
within the tubing. All trials had a starting pressure head of 3.48 kPa, which
was determined from the vertical distance between the water level in the
aquarium and the top of the overflowing beaker.

A live hagfish was gently placed in the aquarium, and 40-90 s after the
start of the siphon the hagfish was pinched on the tail with padded forceps to
induce sliming (Fudge et al.,
2005). A video camera and VCR recorded the display on the
top-loading balance for later review. Outputs from an external timer and a
second camera filming a view of the aquarium were recorded simultaneously on
to the same tape so that data from the balance could be correlated with events
in the tank and time-stamped. Recording was stopped after the balance reached
its upper limit (3000 g).

Water flow rates were determined from the change in mass of water in the
bucket and the time interval between mass measurements. To adjust for the
decreasing pressure head as water flowed from the aquarium, we calculated
standardized water flow rates (ml s-1 kPa-1) over time
by dividing each flow rate measurement by the pressure head at the time of the
measurement. All subsequent calculations involving flow rates used these
standardized values. The siphon system consisted of two components in series
that contributed to the total resistance (R) that the system
presented to the flow of water: the gills (test tube brush or fish head gills)
and the narrow tubing connected to the gills. That is,
Rsystem=Rgills+Rtube.
Measurements of flow rates with and without the gills present were used to
calculate gill resistance relative to the rest of the siphon, and the pressure
drop across the gills. For the artificial gill setup, the test tube brush was
removed from its thick polyvinyl tube housing to achieve a gill-less
condition. In the fish head setup, the gills were removed by pulling off the
dental dam holding the fish head and removing the entire head from the PVC
pipe.

Apparatus for measuring the removable mass of slime produced from mixing
slime exudate in seawater, consisting of a 50 ml beaker mounted on a rotary
shaker. A plastic disk fitted with radial spikes hanging on a wire was used to
collect removable mass.

High-speed video of slime release

Hagfishes were transferred from their holding tanks to a 20-litre aquarium
filled with unfiltered, cold (9°C) seawater. Sliming was initiated by a
quick pinch on the body using long forceps. Digital video of the sliming event
was captured at 125 frames s-1 using a Redlake MotionScope digital
high-speed video camera (Redlake-DuncanTech, Auburn, CA, USA). Close-ups of
slime release from glands were filmed by constraining hagfish in a specially
designed tube that the hagfish voluntarily entered in their holding tank. The
50 mm-diameter tube was 300 mm long and had a window cut in it that allowed us
to focus in on a single gland with a 43.5-mm fish-eye macro zoom lens. The
window also allowed us to stimulate the skin of the hagfish with forceps or a
mild electrical shock (the latter worked best) to induce the sliming response.
Two trials using constrained hagfish were clear enough and at the proper
orientation to allow us to calculate the velocity of slime exudate expulsion
from the slime gland. For velocity measurements, time was measured by the
number of frames, and distance was calibrated using the checkerboard pattern
on the tubing that held the hagfish.

Convective mixing effects and slime collapse

In the high-speed video trials using constrained hagfish, we observed that
exudate released by the hagfish did not hydrate fully, as indicated by it
remaining opaque and sinking to the bottom of the aquarium. This observation
led us to test the hypothesis that some convective mixing is required for
proper slime hydration and formation. To test this hypothesis, we conducted
two additional kinds of video trials in which we filmed the introduction of
freshly collected slime exudate into still seawater either using a spatula or
via injection with a syringe fitted with a shortened 18-gauge needle.
The capture rate for these trials was 60 frames s-1.

We also assessed the effect of mixing on slime formation using a `removable
mass' assay modified from Koch et al.
(1991). A small volume (0.12
ml) of slime exudate stabilized in a high osmotic strength buffer
(Downing et al., 1984) was
injected into 50 ml of artificial seawater on a shaker table set at 200 revs
min-1. After shaking for a precise amount of time (0, 10, 20, 40,
80, 160, 320, or 640 s), a custom hook, which was placed in the beaker before
the addition of slime, was removed (Fig.
3). Removable mass was quantified by weighing the hook and
adherent slime and subtracting the mass of the hook.

Results

Slime increases gill resistance by one to three orders of
magnitude

The relationship between the pressure head, flow rate and resistance in the
siphon system can be described by a version of Ohm's Law for fluid flow:
(1)

where ΔP is the pressure head,
Q̇ is the flow rate, and R is
the resistance. Standardized water flow rates, which we will call
Q̇p, are given by
Q̇/ΔP. Consequently, Eqn
1 can be written in terms of
Q̇p, and then rearranged to
give:
(2)

where Rgills is the resistance of the gills and
Rtube is the resistance of the tubing. Using measurements
of water flow rates with and without the gills present, we determined the
relative magnitudes of Rgills and
Rtube. The relative resistance of the gills is given by:
(3)

and the relative resistance of the tubing is simply:
(4)

For the artificial gills, the mean flow rate without gills was 8.3 ml
s-1 kPa-1, while the mean rate with gills present was
7.9 ml s-1 kPa-1; thus, Rgills,rel
is 0.044±0.0037 (mean ± s.d.; N=3), and
Rtube,rel is 0.956. That is, the tube resistance is
approximately 20 times greater than the artificial gill resistance, which
accounts for only 4% of the total resistance in an unslimed system. Because
the rockfish heads used in the fish head trials varied in size, the relative
resistance of the real fish gills was more variable, ranging from 0.061 to
0.15 (mean ± s.d., 0.11±0.047; N=3). The pressure drop
across the gills was found by multiplying the relative gill resistance by the
mean pressure head in the trial. Mean pressures (± s.d.) across the
artificial gills (0.17±0.014 kPa; N=3) and real fish gills
(0.35±0.16 kPa; N=3) were comparable to pressures found during
normal ventilation in other fishes (e.g. white sucker Catostomus
commersoni, 0.2 kPa; carp Cyprinus carpio, 0.5 kPa)
(Saunders, 1961).

The effects of hagfish slime on (A) water flow rates and (B) brush
resistance in the artificial gill analogue. Slime release occurred at 40-60 s;
three trials are shown separately, and the data have been normalized to their
pre-slime values. Note the log scale for normalized resistance.

Flow rate data from the sliming trials can be used to determine how hagfish
slime affects gill resistance, if we assume that the gills intercept all of
the slime so that tube resistance remains constant throughout the trial. This
assumption is reasonable, considering our observations on the slime vacuum's
suction of released slime: most of the slime was stopped at the brush in the
gill model or inside the mouth of the fish head. In some instances, slime
protruded from the fish's mouth at the end of the trial. Inspection of the
slimed gills revealed mucus and threads coating and caught up in the gills
(Fig. 4). So, assuming that all
changes in system resistance are due to changes in gill resistance, we can
derive an expression for the absolute resistance of the gills for a given flow
rate, at any time during the trial. First, we must calculate the absolute
magnitude of the constant Rtube:
(5)

We know Rtube,rel (Eqn 4), and, because we assume that
Rtube remains constant, we can calculate its absolute
magnitude using data on the pre-slime conditions in the system. Rearranging
Eqn 2 (Ohm's Law) and indicating initial conditions before the gills are
exposed to slime (denoted by the zero subscript) gives:
(6)

We define Rtube as the constant C, and
substitute Eqn 6 into Eqn 5 to get the constant value:
(7)

Equation 2 can now be written in terms of the flow rate and the gill
resistance as functions of time (t):
(8)

Rearranging gives:
(9)

which we can use to calculate gill resistance during the experiment from
the flow rate data.

All trials showed slowed water flow and an increase in gill resistance
following slime release (Table
1). Flow rate and resistance data are presented as normalized
values, Q̇p,norm and
Rgills,norm, obtained by dividing
Q̇p(t) and
Rgills(t) by their mean pre-slime values. The
start of slime suction, as observed from video recordings of the aquarium,
corresponded well with abrupt changes in flow and resistance. Slime uptake
into the artificial gill corresponded with a decrease in flow rate by a factor
of 70-80 (Fig. 5A) and an
increase in resistance of approximately three orders of magnitude
(Fig. 5B). Two trials with the
fish head setup were usable for data analysis. In these trials, slime caused
the flow rate to decrease by a factor of 4-8
(Fig. 6A) and the gill
resistance to increase by one to two orders of magnitude
(Fig. 6B).

The effects of hagfish slime on (A) water flow rates and (B) gill
resistance in the gills of an isolated rockfish head. Slime release occurred
at ∼95 s; results from two fish heads are shown separately, and the data
have been normalized to their pre-slime values. Note the log scale for
normalized resistance.

(A-D) High-speed video images of the local release of slime exudate
(arrows) from a hagfish after it has been pinched with forceps. A-D show
different hagfish.

Slime is locally and forcefully released

Filming hagfish sliming at 125 frames s-1 revealed that release
of exudate occurs only from glands near the point of contact, as opposed to
global release from all of the glands (Fig.
7A-D). These trials also suggested that exudate appears to be
forcefully ejected from the slime gland, as opposed to simply oozing out
(Fig. 8). To confirm this
result, we filmed slime release from constrained hagfish, which allowed us to
focus in on single slime glands. These trials clearly indicate that slime is
indeed forcefully ejected from the glands
(Fig. 9). The jet velocities
measured in two different trials were 0.17 and 0.18 m s-1.

Slime hydration requires convective mixing

Slime exudate introduced into still seawater by a spatula or syringe in the
absence of mixing failed to form a full mass of hydrated slime. The exudate
remained opaque in the water after slipping off the spatula
(Fig. 10A) or being ejected
from the syringe needle (Fig.
10B) and typically fell to the bottom of the tank. In removable
mass trials, mixing duration had a positive effect on removable slime mass up
to about 80 s, after which removable mass tapered off
(Fig. 11). The minimal amount
of hydrated slime produced from short periods of stirring corroborates the
results from our spatula and syringe trials. These trials were conducted using
slime exudate stabilized in a high osmotic strength buffer, which undoubtedly
increased the hydration time of the slime compared with fresh exudate. While
the time to peak hydration is therefore not applicable to slime release in
vivo, the hump-shaped curve is still revealing about the evolution of
slime structure and mechanics over time.

Discussion

We tested the hypothesis that hagfish slime functions to deter
gill-breathing predators and found that the slime appears to be capable of
clogging fish gills and impairing the flow of water through them. The effects
of the slime on flow rates were apparent in each trial, but the magnitude of
the response varied between trials. This is not entirely surprising as the
amount of hagfish slime produced was probably variable among different trials.
As an example, Fig. 6B shows
that resistance at the gills of one fish head increased by a factor of 20,
which is not a trivial effect; however, the gills of the second fish
experienced a 100-fold increase. The slime effectively increased the
resistance of a gill analogue and real gills, consequently slowing the passage
of water through them; this result is consistent with the sieve model of
hagfish slime structure and function presented in Fudge et al.
(2005). The slime's greater
effect on the artificial gill model is likely to be due to the multi-layered
and densely packed bristles of the test tube brush, which would catch more
slime than the single layer of wider-spaced gill rakers in the fish head.

Close-up of slime release from a single slime gland of a hagfish
constrained in a tube with a window cut in it. These events were filmed at 125
frames s-1, and the mean jet velocity was 0.17 m s-1.
Scale bar, 5 mm.

Also, the smaller area of the model gill's opening compared with the open
area of the fish mouth makes the model gills easier to block with a given
amount of slime; the slime is more concentrated in this small area, and water
flow is impaired to a greater extent.

For a live fish predator, sustained low water flow over the gills might
lead to insufficient oxygen delivery and reduced gas exchange. Furthermore,
the increase in diffusion distance across the gills caused by a slime coating
should also decrease gas exchange, as diffusion rates are inversely
proportional to distance (Fick's Law)
(Vogel, 2003). This hypothesis
will be tested in future experiments using respirometry of live fish exposed
to hagfish slime. The potential for suffocation through one or both of these
mechanisms might discourage gill-breathing predators from preying on
hagfish.

Slime exudate introduced into still seawater from (A) a spatula or (B)
injection from a syringe fails to hydrate as it does in vivo.

High-speed video of free-swimming hagfish revealed that they do not
generally release slime and then hide within it
(Fig. 12). The local release
of exudate supports this idea; simultaneous slime release from all of the
glands would likely be more effective at producing a mass of slime for an
instant refuge. Hagfish have an ingenious behaviour, however, that implies
that they do occasionally have to free themselves from their own slime.
Covered in slime and facing eventual suffocation, a hagfish will tie its body
in a knot and pass the knot toward its head to slough off the slime
(Strahan, 1963;
Martini, 1998). While not a
protective shroud, the behaviour of slime release suggests that it may have a
more active role in defending hagfish against predators. When pinched, slime
glands near the region of contact respond by forcefully ejecting exudate as a
coherent jet. It is possible that the combination of local and forceful
release of slime is functionally important in `targeting' the gills of an
attacking fish predator.

To test this argument, we address here the mechanics of slime release in
more detail. We develop a simple model of slime ejection, determining whether
the muscular contraction of the gland capsule is sufficient to eject the
exudate at the velocity observed or whether the surrounding myotomal muscle
must also be recruited. The first thing we need to know is the pressure that
the gland can generate. This can be calculated from the Law of Laplace for a
sphere:
(10)

where σsphere is the wall stress, p is the
pressure, r is the radius and d is the wall thickness. Using
a typical muscle stress of 200 kPa, a gland radius of 0.65 mm and a wall
thickness of 45 mm (Lametschwandtner et
al., 1986), we get a pressure inside the gland of 28 kPa, or about
double the blood pressure of a mammal.

To calculate the velocity of the exudate as it exits the gland, we use the
Hagen-Poiseuille equation for flow through a pipe:
(11)

where Q̇ is flow, a is the
radius of the pipe (45 μm), Δp is the pressure head, μ is
the dynamic viscosity and l is the duct length. Since we already know
the jet velocity (0.175 m s-1) from high-speed video, we can use
this equation to calculate the viscosity of the exudate. If it gives us a
reasonable value, then we know that the muscular gland capsule is capable of
ejecting the slime without help from the surrounding myotomal muscle.
Rearranging the equation above, we get:
(12)
and with a pressure head of 28 kPa (from LaPlace), a pipe radius of 45 μm
and a duct length of 500 μm (Spitzer
and Koch, 1998), we get a viscosity of 0.08 Pa s, which is about
60 times the viscosity of seawater at 10°C and not an unreasonable value.
If the calculation predicted a viscosity considerably less than water, then
clearly we would need to invoke another source of pressure. Our estimates
indicate, however, that the gland capsule can eject a fluid with a viscosity
60 times that of seawater at the velocities we have measured; thus, another
mechanism, such as compression of the gland via contraction of nearby
myotomal muscle, is not required to explain our data.

The removable mass of slime plotted against stirring time demonstrates that
stirring is required for proper slime hydration and cohesion and that
excessive stirring eventually leads to slime collapse. Values are means±
s.e.m.

High-speed video (shot at 125 frames s-1) of a sliming event
demonstrating that released slime rarely envelops the hagfish and often is
dispersed by an evasive manoeuvre that mixes the exudate with seawater.

After exudate is discharged into seawater, convective mixing is essential
for rapid hydration and full expansion of the slime. The Reynolds number
(Re) of the exudate jet is informative on this point. Using the
values for exudate viscosity and jet velocity that we calculated above, and
the gland duct diameter, Re within the duct is ∼0.1. Because flow
immediately outside the duct is unlikely to differ much from the flow inside
the duct, the Re indicates that the exudate jet is laminar. As a
result, the exudate experiences very little mixing from inherent turbulence in
the jet despite its seemingly forceful ejection. Also, given the relatively
large size-scale of the slime, diffusion alone is insufficient to cause
formation once the exudate is in seawater. In nature, convective mixing is
likely fulfilled by the hagfish itself, as escape behaviours often include
vigorous thrashing after slime release. While this requisite mixing appears at
first to be a limitation, it may serve an important function: if expansion
were faster, the slime would form closer to the slime gland pore. This could
decrease the distance that the slime is shot and potentially even clog the
gland pore. The laminar character of the exudate jet and the full formation of
slime some time after release from the gland also support the idea that the
jet is more important in the targeting of predator gills than other functions,
such as mixing.

Removable mass trials showing the non-linear relationship between the
amount of final slime product and stirring time underscore the convective
mixing result. They also indicate, however, that mixing past a certain point
decreases the mass of slime produced. This agrees with previous studies that
have demonstrated that the slime collapses when it is disturbed
(Ferry, 1941;
Fudge et al., 2005). In a
future study, we will explore in more detail the mechanism by which the mucins
and fibrous threads interact with seawater and each other to form fully
hydrated slime.

The sieve model of hagfish slime in which water is loosely bound is
consistent with the anti-predator role of the slime when one considers the
functional trade-offs between a slime that binds water loosely versus
a gel that binds it tightly. Hydration is slower in a loosely binding slime,
meaning the exudate jet can travel farther than it would if it had a greater
affinity for water. In addition, the resulting slime has a greater volume and
is less mechanically coherent. Such slime may have more opportunity to
initially stick to the gills of a predator and tangle between the gill rakers
compared with a more coherent and smaller slime mass. Prolonged agitation of
the slime from any subsequent thrashing will also cause the slime to collapse
more completely on the gills, as the results of our removable mass experiments
imply. At one extreme, slime with little coherence might be more likely to
catch on the gills but may not interfere much with respiratory flow. At the
other extreme, coherent slime might effectively block water flow but may be
ineffective at lodging in the gills in the first place. In addition, a tight
plug of slime would be easier for a fish to dislodge via `coughing'.
Thus, the strength of the interaction between the slime and seawater may be a
compromise among several requirements for effective anti-predator activity.
While the focus of the present study has been the anti-predator function of
hagfish slime, the slime should be equally effective at endangering
gill-breathing competitors. Hagfish also release slime during feeding
(Martini, 1998) and this could
serve to deter competitors from imposing themselves on a hagfish's meal.

Conclusions

We demonstrate here that hagfish slime can clog fish gills, which increases
gill resistance and slows water flow through them. The potential for entrapped
slime to interfere with gill respiration suggests that the slime may have
evolved to deter gill-breathing animals from preying on hagfish. We have shown
that the release of slime exudate is local and that its forceful ejection from
the slime gland can be accomplished by contraction of the gland capsule muscle
alone. Once slime is released into the water, the extent of its hydration and
expansion depends on the amount of convective mixing in the water. The
mechanical consequences arising from different models of how tightly water is
bound to the slime imply that hagfish slime's loose water binding is
functionally important in defending hagfish against gill-breathing
predators.

Symbols and abbreviations used

a

duct radius

C

constant value of Rtube

d

wall thickness

l

duct length

p

pressure inside gland

Q̇

flow rate

Q̇
p

standardized flow ratey

Q̇
p,no gills

standardized flow rate without gills present

Q̇
p,norm

normalized flow rate

Q̇
p,0

pre-slime standardized flow rate

Q̇
p,with gills

standardized flow rate with gills present

r

gland radius

R

resistance

Re

Reynolds number

Rgills

gill resistance

Rgills,norm

normalized gill resistance

Rgills,0

pre-slime gill resistance

Rgills,rel

relative gill resistance

Rsystem

siphon system resistance

Rsystem,0

pre-slime system resistance

Rtube

tubing resistance

Rtube,rel

relative tubing resistance

t

time

Δp

pressure head in the gland duct

ΔP

pressure head in the slime vacuum

μ

dynamic viscosity

σsphere

gland wall stress

ACKNOWLEDGEMENTS

We thank the staff of the Bamfield Marine Sciences Centre for assisting in
the collection and care of hagfish. This work was supported by an NSERC
operating grant to J.M.G., a Killam doctoral fellowship to D.S.F. and an NSERC
undergraduate research award to J.L.